Fractional Maximal Functions in Metric Measure Spaces

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1. [1] D. R. Adams, A note on Riesz potentials, Duke Math. J. 42 (1975), 765-778. Zbl0336.46038
2. [2] D. R. Adams, Lecture Notes on Lp-Potential Theory, Dept. of Math., University of Umeå, 1981. 
3. [3] D. R. Adams and L. I. Hedberg, Function Spaces and Potential Theory, Springer-Verlag, Berlin Heidelberg, 1996. 
4. [4] S. M. Buckley, Is the maximal function of a Lipschitz function continuous?, Ann. Acad. Sci. Fenn. Math. 24 (1999), 519-528. 
5. [5] S. M. Buckley, Inequalities of John-Nirenberg type in doubling spaces, J. Anal. Math 79 (1999), 215-240.[Crossref] Zbl0990.46019
6. [6] D. Edmunds, V. Kokilashvili, and A. Meskhi, Bounded and Compact Integral Operators, Mathematics and its Applications, vol. 543, Kluwer Academic Publishers, Dordrecht, Boston, London, 2002. Zbl1023.42001
7. [7] J. García-Cuerva and J. L.Rubio De Francia, Weighted Norm Inequalities and Related Topics, North-Holland Mathematics Studies, 116. Notas de Matemática, 104. North-Holland Publishing Co., Amsterdam, 1985. 
8. [8] A. E. Gatto and S. Vági, Fractional integrals on spaces of homogeneous type, Analysis and Partial Differential Equations, C. Sadosky (ed.), Dekker, 1990, 171-216. Zbl0695.43006
9. [9] A. E. Gatto, C. Segovia, and S. Vági, On fractional differentiation and integration on spaces of homogeneous type, Rev. Mat. Iberoamericana 12 (1996), no. 1, 111-145. Zbl0921.43005
10. [10] I. Genebashvili, A. Gogatishvili, V. Kokilashvili and M. Krbec, Weight Theory for Integral Transforms on Spaces of Homogeneous Type, Addison Wesley Longman Limited, 1998. Zbl0955.42001
11. [11] A. Gogatishvili, Two-weight mixed inequalities in Orlicz classes for fractional maximal functions defined on homogeneous type spaces, Proc. A. Razmadze Math. Inst. 112 (1997), 23-56. Zbl0881.42016
12. [12] A.Gogatishvili, Fractional maximal functions in weighted Banach function spaces, Real Anal. Exchange 25 (1999/00), no. 1, 291-316. Zbl1015.42014
13. [13] O. Gorosito, G. Pradolini, and O. Salinas, Boundedness of the fractional maximal operator on variable exponent Lebesgue spaces: a short proof, Rev. Un. Mat. Argentina 53 (2012), no. 1, 25-27. Zbl1256.42030
14. [14] P. Hajłasz, Sobolev spaces on an arbitrary metric space, Potential Anal. 5 (1996), no.4, 403-415. Zbl0859.46022
15. [15] P. Hajłasz, Sobolev spaces on metric-measure spaces, In: Heat kernels and analysis on manifolds, graphs, and metric spaces (Paris, 2002), pp. 173-218, Contemp. Math. 338, Amer. Math. Soc. Providence, RI, 2003. Zbl1048.46033
16. [16] P. Hajłasz and P.Koskela, Sobolev met Poincaré, Mem. Amer. Math. Soc. 145 (2000), no. 688 Zbl0954.46022
17. [17] T. Heikkinen, J. Kinnunen, J. Nuutinen, and H. Tuominen, Mapping properties of the discrete fractional maximal operator in metric measure spaces, to appear in Kyoto J. Math. Zbl1280.42012
18. [18] T. Heikkinen and H. Tuominen, Smoothing properties of the discrete fractional maximal operator on Besov and Triebel-Lizorkin spaces, http://arxiv.org/abs/1301.4819 Zbl1295.42004
19. [19] J. Kinnunen and E. Saksman, Regularity of the fractional maximal function, Bull. London Math. Soc. 35 (2003), no. 4, 529-535. Zbl1021.42009
20. [20] N. Kruglyak and E. A.Kuznetsov, Sharp integral estimates for the fractional maximal function and interpolation, Ark. Mat. 44 (2006), no. 2, 309-326. Zbl1156.42308
21. [21] M. T. Lacey, K. Moen, C. Pérez, and R. H. Torres, Sharp weighted bounds for fractional integral operators, J. Funct. Anal. 259 (2010), no. 5, 1073-1097.[WoS] Zbl1196.42014
22. [22] P. MacManus, Poincaré inequalities and Sobolev spaces, Proceedings of the 6th International Conference on Harmonic Analysis and Partial Differential Equations (El Escorial, 2000), Publ. Mat. 2002, 181-197. 
23. [23] P. MacManus, The maximal function and Sobolev spaces, unpublished preprint 
24. [24] B. Muckenhoupt and R. L. Wheeden, Weighted norm inequalities for fractional integrals, Trans. Amer. Math. Soc. 192 (1974), 261-274. Zbl0289.26010
25. [25] E. Nakai, The Campanato, Morrey and Hölder spaces on spaces of homogeneous type, Studia Math. 176 (2006), no. 1, 1-19. Zbl1121.46031
26. [26] C. Pérez and R. Wheeden, Potential operators, maximal functions, and generalizations of A1, Potential Anal. 19 (2003), no. 1, 1-33. Zbl1027.42015
27. [27] E. Routin, Distribution of points and Hardy type inequalities in spaces of homogeneous type, preprint (2012), http://arxiv.org/abs/1201.5449 Zbl1305.42018
28. [28] E. T. Sawyer, R. L. Wheeden, and S. Zhao, Weighted norm inequalities for operators of potential type and fractional maximal functions, Potential Anal. 5 (1996), no. 6, 523-580. Zbl0873.42012
29. [29] R. L. Wheeden, A characterization of some weighted norm inequalities for the fractional maximal function, Studia Math. 107 (1993), 257-272. Zbl0809.42009
30. [30] D. Yang, New characterizations of Hajłasz-Sobolev spaces on metric spaces, Sci. China Ser. A 46 (2003), no. 5, 675-689.[Crossref] Zbl1092.46026